Problem: Solve for $y$, $- \dfrac{5y - 4}{y - 6} = \dfrac{1}{7} $
Explanation: Multiply both sides of the equation by $y - 6$ $ -(5y - 4) = \dfrac{y - 6}{7} $ Multiply both sides of the equation by $7$ $ -7(5y - 4) = y - 6 $ $-35y + 28 = y - 6$ $28 = 36y - 6$ $34 = 36y$ $36y = 34$ $y = \dfrac{34}{36}$ Simplify. $y = \dfrac{17}{18}$